|
| |
|
|
A150197
|
|
Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 0, 1), (0, 0, -1), (0, 1, 1), (1, 0, 0)}
|
|
0
| |
|
|
1, 2, 6, 21, 79, 309, 1249, 5169, 21765, 92972, 401689, 1751826, 7701210, 34083739, 151727337, 678869577, 3050982026, 13766056536, 62331604383, 283125629691, 1289705251153, 5890141647542, 26964131637716, 123704614672581, 568653445996345, 2618817366720532, 12080886988814808, 55818172843274938
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
LINKS
| A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.
|
|
|
MATHEMATICA
| aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]
|
|
|
CROSSREFS
| Sequence in context: A148491 A026737 A111279 * A150198 A033321 A050203
Adjacent sequences: A150194 A150195 A150196 * A150198 A150199 A150200
|
|
|
KEYWORD
| nonn,walk
|
|
|
AUTHOR
| Manuel Kauers (manuel(AT)kauers.de), Nov 18 2008
|
| |
|
|
